Question

Evelyn went shopping with half of her monthly allowance. She spent $39.95 on a dress and 3/7 of the remainder on some accessories. Evelyn had 30.60 left after shopping. What is Evelyn's monthly allowance?

Answer 1

Evelyn monthly allowance is $187.

Explanation:

Let the monthly allowance be 'x'.

Given:

Money taken with for shopping =
`(x)/(2)`

Money spent of dress = $39.95

Also Given:

3/7 of the remainder on some accessories.

Money spent on accessories is equal to
`(3)/(7)` times Difference of monthly allowance and Money spent of dress.

framing in equation form we get;

Money spent on accessories =
`(3)/(7)*((x)/(2)-39.95)`

Also Given:

Money left after shopping = $30.60

Now we know that;

Money taken with for shopping is equal to sum of Money spent of dress and Money spent on accessories and Money left after shopping.

framing in equation form we get;

`(x)/(2)=39.95+(3)/(7)((x)/(2)-39.95)+30.60\\\\(x)/(2)=39.95+(3x)/(14)- 17.12 +30.60`

Combining like terms we get;

`(x)/(2)-(3x)/(14)=39.95-17.12+30.60\\\\(x)/(2)-(3x)/(14)= 53.43`

Now we will make denominator common using L.C.M

`(x* 7)/(2*7)-(3x*1)/(14*1)= 53.43\\\\(7x)/(14)-(3x)/(14)= 53.43\\\\(7x-3x)/(14)=53.43\\\\(4x)/(14)=53.43\\\\4x=53.43*14\\\\x= (53.43*14)/(4) = \$187`

Hence Evelyn monthly allowance is $187.